Why Range Voting is Better than Approval Voting

1. What they are:Range voting:
In an N-candidate election, each vote
is an N-tuple of numbers each in the range 0 to 99.
The Kth number in the tuple is a "score" for candidate K.
You take the average of all the Kth entries to find
the average score for candidate K. The candidate
with the highest average score wins.
(Voters are allowed to leave an entry blank to denote
"don't know anything about that candidate." Blank entries
not incorporated into average.)

Approval voting:
Same thing as range voting, except
each number, instead of being anywhere from 0 to 99 has to be
either 0 ("disapprove") or 1 ("approve").
[Thus, approval voting is really just a special case of range voting.]

2. Simplicity:
Approval voting wins this one: it obviously is simpler.
(But not by as much as you might think, since Jan Kok showed a
simple way to
use any voting machine capable of handling multiple plurality contests – i.e.
all voting machines in the USA – to perform "single digit" range elections.
On lever machines, optical scan machines, and many kinds of punch card machines,
the voter finds it extremely easy and straightforward to use any of
Plurality, Approval, or single-digit Range Voting, often with no real advantage in
simplicity for either.)

In fact, it has been argued that approval voting actually is simpler
– both to understand and to count –
than plurality voting:
since no special caution is necessary to detect "overvotes" and discard them.
("Overvotes," and in fact every possible combination of approval and disapproval
votes, are perfectly legal under AV – there is no artificial distinction
between "legal" and "illegal" votes that can be used to "justify" massively
discriminatory "ballot spoilage" manipulations.)

3. Expressivity and Honesty:
Obviously, with range voting, you are free to cast an "approval style" vote
by only using 99s and 0s, never using anything in between – if you so desire.
(And in fact, "strategic" voters usually would do exactly this.)
So range voters clearly can be either equally expressive, or
more expressive, than approval voters.

The more information voters can submit in their vote, the better we expect
the results of the election (from their point of view) to be.

So the question is: is approval voting better because it is simpler, or is range
voting better because it allows more expressive freedom?

The answer hinges on how many voters will choose to be "honest" and how many will be
"strategic" (and how many will adopt some compromise). That is because if
all voters are strategic, then range voting will simply degenerate to approval voting
and then there would be no reason to adopt RV, since it is more complicated.

However, Doug Greene and W.D.Smith did a range voting election among random
voters emerging from polls in the 2004 Presidential election in New York State
(#82 here).
We found that (with 90% confidence) less than 33% of range voters vote
approval-style (central estimate: 25-26%),
and, further, that less than 43% even use the full range
(i.e. include both a 99 and a 0 in their vote). We told them to vote as they
actually would if the real election were being held using range voting, and I
know I told my voters things like "the only meaning of the numbers you supply are
the numbers themselves; your job is to choose them to make it the most likely
the election will turn out in a way you like." Now while I concede that
the 25% and 43% would undoubtably rise if our voters were exposed to more
information and thought longer than 1 minute (most or all of them had never heard of
range voting before they met us), it seems clear there will always be a substantial
fraction of range voters who do not want to vote approval-style.

This finding was surprising news to many in the voting research field.
There is evidently a large psychological urge to be honest
and that urge seems to affect range voters to a far greater degree than plurality voters.
(It is known from National Election Study data that fewer than 1 in 10 of
year-2000 voters whose favorite was Nader, actually voted for Nader; same thing happened
with Buchanan – i.e. plurality voters are very strategic/dishonest. Interesting
contrast, eh? Range voting somehow stimulates people's honesty more than plurality does.)

Incidentally, this is not just purely an irrational quirk of human beings. There also
is logic behind it. Specifically, if you are going to be strategically dishonest
in your vote, then some parts of that vote matter more than others.
Namely, the parts which concern the 2 or 3 candidates you think are most likely to win.
For them, it makes a good deal of sense to exaggerate and rate them all 0s or 99s.
But the "payoffs" for dishonesty about the remaining candidates
(whom you think have extremely tiny chance of winning) are extremely small.
The typical voter thinks: "why bother? I'll just be honest about them."
And he is right to think so.

Now. Given that we know this fact about human beings and their observed behavior,
it seems clear that range voting is better than approval voting, because
it allows more humans to satisfy their urges for honesty, and therefore
will produce election results that more honestly reflect voters' true opinions.

This can be a big effect favoring range over approval, and it can lead to
dramatically different vote counts.

4. Nursery effect:
In particular, a dramatic experimental difference between range and approval voting –
which appears to be a consequence of exactly the sort of "weighing the
relatively importance of strategy and honesty for different candidates" thinking
we just described – is the "nursery effect." That is, small "helpless infant"
third parties all receive
hugelylarger totals
under range voting than approval voting.
That (we hypothesize) is due to honest range
voters who under approval voting feel forced to dishonestly
give those parties exactly zero. This effect causes small third parties to be capable of
attracting donors and supporters and candidates – and therefore to be capable
of growing into big "grown-up" parties with range voting. With approval voting,
it may be that third parties will simply never be able to break out of infancy.

This is an advantage of range voting over
approval voting from the point of view of third parties –
all US third parties would have gotten 2% or less under approval voting in 2004
and hence qualify as "helpless infants."
But, e.g, Michael Badnarik, the Libertarian party's presidential candidate, who got 0.3% under
plurality in 2004, would have gotten 0.6% under approval and 9% under range.
Range from his view was 15 times better than approval.

Why do we care about Michael Badnarik's happiness? Several reasons. First, third parties
as the ones most victimized by the unfair plurality system, are going
to play an essential role in bringing us voting reform. If you ask them
to support approval rather than range, then they won't. If you can't even get support
from those with the most at stake, forget getting anywhere. So you won't
get voting reform. Game over, you lose. This trumps every other
argument about range versus approval voting.

Second, it seems to us healthier to have a voting system in which small third parties are capable
of growing into big ones. That prevents permanent unhealthy sterile 2-party domination,
and more generally prevents parties from getting into power,
becoming corrupt, and then staying in power without ever having to fear being
supplanted by newcomers.

5. When is the range-favoring approval-disfavoring effect largest?
When we have an election with a large number of candidates,
and have a lot of honesty in our voters, then range does maximally
better than approval voting. (Indeed in this regime,
even Borda
voting is superior to approval.)
But in elections with small numbers
of candidates and highly strategic voters,
range and approval voting act the same.
Note that the Iowa 2008 caucuses are likely to fall exactly in the former, maximally-range-favoring,
regime.

Even a small percentage of honest range voters can make a big difference in quality.
To illustrate how that can be, consider the following artificial example.
Suppose there are 20 candidates, 7 fairly-universally agreed to be good and 13
fairly-universally agreed to be bad. Rational approval voters (or strategic range voters)
will approve of all 7 good ones but none of the 13 bad ones. Result: 7-way tie.
This tie will then be broken by random chance, or by the effects of a tiny number of irrational or
dishonestly biased voters (such as bribed ones, or family members of the candidates)
with the result that, on average, the 4th-best candidate will be elected.
Now suppose that a fraction (and even only, say, 5% of the population, will work excellently)
of the voters are honest range voters, and there is a collectively perceptible quality
gradient among the good 7. In that case, the best candidate, not the 4th best, will win.

If we say to the voters: "sorry, we are going to force you all to
strategically-exaggeratingly employ approval-style votes (0 and 99 only,
intermediate values forbidden)" then we intentionally sacrifice all
chance of this enormous quality improvement. What benefit is worth that cost?

6. California 2003: an election with 135 candidates.
Suppose most voters knew something about, say, 5 of the 135 candidates, and
nothing about the other 130. With approval voting, they would probably "play it safe"
by disapproving of all the unknowns, resulting in a huge bias against lesser-known
candidates, as opposed to what we want, i.e. a bias against lesser-quality candidates.
(That behavior was common in the sample of people I polled.
In the version of range and approval I have advocated above
they could leave those candidates blank. But it is an experimental fact that
many voters prefer zeros to blanks in such cases.)

With range voting, they could give the unknowns all X, where X is a number they choose
to fill in everything else with.
For many voters quite possibly X would not be zero. This would lessen this bias.

In riposte it was pointed out to me that Approval voters could simulate (a noisier
version of) range voting by tossing appropriately biased dice to select whether
to approve each candidate. However – be realistic.
That is not going to happen in the real world.

So: range voting handles ignorant voters better than approval voting does – the latter
tends to introduce more artificial biases in that situation.

7. Bayesian Regret (For Statistics Nerds):
Approval voting does quite badly (measured by Bayesian Regret)
compared to many other more expressive voting systems such
as Borda and Black, when there are 4 or more candidates and we have honest voters.
The more candidates, the worse approval does, with a very big gap developing.
This was shown in computer experiments by Merrill, later confirmed by me.

Approval is better than these systems – for strategic voters – but is worse for honest ones.

The joy of range voting is it is better both for honest and
for strategic voters.
Computer Bayesian regret measurements by me show range voting as good or better
than every other voting system tried including Approval, Plurality, IRV, Condorcet, Borda,
in a vast number of different kinds of scenarios with either honest or
strategic voters, whether there are 5 voters or 200, and either 3,4, or 5 candidates,
under different kinds of "utility generators", and with
different levels of "voter ignorance".
(For W.D.Smith's papers on voting see
#56, 59, 76-80 here.)

8. Potential for Ties and Near-tie nightmares:
Remember how Bush v Gore, Florida 2000, was officially decided by only 537 votes,
and this caused a huge crisis? Ties and near-ties are bad.

Exact and "1-off" ties are much less likely in range voting than approval voting, simply because
there is a large range 0-99 rather than 0-1. (Near-ties are probably also less likely,
but not tremendously so.)

9. Unfair advantage for smarter voters?
It was suggested to us that an "advantage" of approval over range
was that in range voting, some voters will be honest and others will be
strategic (i.e. vote approval-style), and the latter will have an "unfair" advantage.
Meanwhile with approval voting, all voters will (to a good approximation) be
forced to act strategic, like it or not. So this "unfairness" would largely vanish.

We reply: if you buy this logic, then it would follow that you also support forcing
voters to vote Democrat or Republican in the present plurality system. Since,
after all, voting third-party is (while honest) strategically stupid. Those
who like third-party candidates and who are stupid enough to honestly say so
are placed at an "unfair" disadvantage and we should force them to vote Democratic
or Republican to protect them from themselves. Right?

Well, no. Nobody supports that. This is not an "unfair" advantage anyhow, since
nobody is forcing any voter to do anything and all voters are treated the same.

Another reply: Any such "advantage" of subset A of voters over subset B of voters,
does not exist if A and B both contain equal fractions of strategic members. Our 2004
study of real-world voters found no evidence that, e.g. supporters of Democratic
presidential candidate John Kerry were any more or less strategic than
supporters of Republican presidential candidate George Bush.
Our study did find that
"third party" voters (i.e. those who gave a positive score to somebody besides
Bush & Kerry) were distinctly less strategic. But this did not mean
that third-party candidates got more of an advantage under approval voting –
instead, they got far more votes with range voting – and
this was due, apparently, to voter honesty, not strategy!
So: this feared phenomenon
simply did not exist in the 2004 election, in reality!

Third reply: What about candidates who have little chance? By forcing voters
to vote all-or-nothing on them (Approval) we get a highly distorted score for them.
This all has nothing to do with "unfair strategic advantages" since for these
candidates any such "advantage" is very small since they aren't gong to win.
So in recompense for this distortion, we gain nothing.

More about this:
The worry that strategic range voters could have more relative power than honest ones, is often raised
as a criticism of range voting and a reason to prefer approval voting.
I think it useful to distinguish strategic voters, who are
trying to get a candidate they like elected, but
feel that casting an exaggerated vote is a better way to accomplish that goal, versus plain dishonest
voters, who are trying to elect a candidate they do not like (e.g. because they
have been bribed). Strategic voters are not so bad because strategic voters with different politics
tend to cancel out, and even if they do not exactly cancel,
a pretty good candidate still tends to win. I find it hard to believe that voters in one
political camp will be systematically more strategic (repeatedly, throughout history,
without any rapid learning going on?!?) than those in a strong rival camp.
Dishonest voters could be serious in some contexts especially, such as
judging skating contests.
For that purpose I would recommend trimmed-mean range voting
which is a variant of range voting
designed to be immune to a certain percentage
of corrupt voters. But trimmed-mean range voting seems inappropriate for large political elections
because of its anti-democratic features (the votes of "extremists" are tossed in the garbage).

10. Mitigation of ignorance/indecisiveness:
By not requiring all-or-nothing ratings, Range Voting mitigates the effects of poor
strategy and voter misjudgement about the candidates. Better than the
misinformed voter not vote his misinformation full-strength, as he must do
in Approval.

Another view of the same thing:
Sometimes someone doesn't know whether or not to vote for someone in
Approval. Approval then forces her to vote a decisiveness that she
doesn't feel. Range Voting lets her vote her indecisiveness. If you don't
know, why should you have to decisively vote all or nothing?

11. Familiarity:
Range Voting is more familiar than Approval Voting, making it easier to "sell"
and more adoptable.
Who has not been asked to rate
something from 0 to 10?

14. Saari's attacks on approval voting:
Mathematician Don Saari raises two criticisms of Approval Voting.
The first is what might be called "indecisiveness." The trouble is,
voters who feel A>B>C are forced to vote as though A=B>C or as though A>B=C.
They have to decide which way to score B – approve or not.
They may, depending on whim, rumors, or whatever – some rather random and
arbitrary-seeming cause –
decide to go predominantly one way or the other, causing a big swing.

That prospect makes Saari uncomfortable.

Now actually, in Bayesian Regret measurements,
approval still works quite well despite this effect. So it is not immediately
clear there is any real ground for discomfort.
Remember, it does not matter whether "Saari is uncomfortable."
What matters is "the Bayesian Regret for all of society."

Saari's second criticism [raised with J.Van Newenhizen:
"The Problem of Indeterminacy in Approval, Multiple and Truncated Voting Systems,"
Public Choice
59,2 (1988) 101-120; responses
& rejoinders 59,2 (1988) 121-131, 133-147, 149],
which is related and is intended
to make the first criticism maximally dramatic, is this.

#voters

Their Vote

9999

A>B>C

1 nut

C>B>A

"Obviously" A should be the winner here.
But with approval voting it is possible
that the 9999 voters will all approve both the excellent A and the mediocre B –
perhaps because of a rumor that the horrible C might win, and they are determined
to prevent that.
Although this is possible, it seems highly unlikely; and
indeed Saari on other occasions, including in email to me, claimed approval voters would
have no reason to do anything other than always approving just one candidate –
Saari was also wrong about that, but he's right that
in small (e.g. 10 or fewer voters)
approval elections with 3 candidates, vote-for-one is a
pretty good strategy.
Anyway, to return to Saari's line of thought:
if all the red candidates get approved, the
mediocre B would win with unanimous approval, even though he
also is unanimously agreed to be mediocre and A is agreed by 9999-to-1 margin to be excellent.

The problem here is all of B's votes are really second-place votes, but approval
"rounds them off" to count as full-approval just like for A.

Both of these Saari-problems are cured, either partially or totally, by range voting:
range voters are not forced to "round off" B to full equality with A.
(If even a few percent rated B slightly below A, this pathology could not happen.)
And wild swings caused by rumors driving biased roundoffs, would diminish.
(A different cure for wild rumor-driven swings is Simmons' DYN
modification of approval.)

Saari called approval voting a "cure worse than the disease,"
on the grounds that it divorces the results of an election from the voters' preferences.
That is, the same voter profile can produce many different results, depending
on where each voter decides to draw the line between approved and non-approved candidates.
Brams, however, viewed this as an advantage, because it gives each voter "sovereignty" over the way
she expresses her preferences.

Well, note that range voting does not perform such a "divorce,"
although it is true that the same preferences with strength information removed
can produce many different results with range voting (depending what preference strengths are used).
Borda voting divorces the results of the election from this strength information.
Range voting does not.

Saari in his book "Chaotic Elections" notes that in, e.g. a perfectly symmetric 3-way cyclic tie,
with approval voting "anybody could win." Saari regards that as a disadvantage of approval voting.
With (continuum) range voting, such ties will generically not happen at all, which I would regard
as an advantage for range voting.